What is the nature of the displacement-time graph of a body moving with constant acceleration?

Displacement – Time graph of a body moving with constant acceleration is as shown in the right side.

Explanation:

Slope of displacement – time graph gives the velocity.

Consider the following graph:

Here AB = Displacement of Body

And OB = Time Taken

Now, Velocity =

But is known as slope of line OA.

We know that in constant acceleration, velocity is changing with time at a constant rate.

Since, Acceleration =

So, slope of displacement – time graph is changing at a constant rate and hence we get a graph like shown at the beginning.